Chapter 7.6, Problem 53PPS

To determine

To find a match to the given graph with the given list of functions

Answer to Problem 53PPS

  $m(x)=f(x)-2$

Explanation of Solution

Given:

  

Also, the parent function is: $f(x)={\left(\frac{3}{2}\right)}^x$

Calculation:

Let,

  $\begin{array}{l}\Rightarrow y=f(x)+n\\ \Rightarrow y={\left(\frac{3}{2}\right)}^x+n\mathrm{....................}(i)\end{array}$

Where n is constant, which needs to be calculated accordingly.

Now, equation ( i ) is compared with the list of functions given.

The above format matches only with one function, which is: $m(x)=f(x)-2\Rightarrow m(x)={\left(\frac{3}{2}\right)}^x-2$

Verification:

Using graphing utility tool, the graph of above function is plotted and compared with the given graph.

(i(ii)

Interpretation:

When both the above graphs are compared, it is clear that they are same, which means the calculations done is correct.

Conclusion:

Hence, the function for the given graph is $m(x)=f(x)-2$ .